infinite_1d_box.py 文件源码

def energy_corrections(perturbation, n, a=10, mass=0.5):
    """
    Calculating first two order corrections due to perturbation theory and
    returns tuple where zero element is unperturbated energy, and two second
    is corrections

    ``n``
        the "nodal" quantum number. Corresponds to the number of nodes in the
        wavefunction.  n >= 0
    ``a``
        width of the well. a > 0
    ``mass``
        mass.

    """
    x, _a = var("x _a")

    Vnm = lambda n, m, a: Integral(X_n(n, a, x) * X_n(m, a, x)
        * perturbation.subs({_a: a}), (x, 0, a)).n()

    # As we know from theory for V0*r/a we will just V(n, n-1) and V(n, n+1)
    #   wouldn't equals zero

    return (E_n(n, a, mass).evalf(),

            Vnm(n, n, a).evalf(),

            (Vnm(n, n - 1, a)**2/(E_n(n, a, mass) - E_n(n - 1, a, mass))
           + Vnm(n, n + 1, a)**2/(E_n(n, a, mass) - E_n(n + 1, a, mass))).evalf())